NAMES:
10.3 – Exponential Growth
You have just joined a book club. You currently have one book in your library. At the end of
the first week the club sends you another book. At the end of each successive week the club sends you
enough books so that the total number of books you have is doubled. [That is, at the end of the first
week they sent one so that your library doubled in size to two. At the end of the next week they will
send two so that you will then have four altogether, etc.]
1. If you name the time you started t = 0 and your initial library’s size (one) to be P0, find a formula
for the number of books that you have at the end of week t = n.
2. How many books will you have at the end of:
one month (four weeks)?
three months (13 weeks)?
six months (26 weeks)?
one year (52 weeks)?
3. Suppose the books average a thickness of one inch per book. You don’t have time to read them
because you’re spending all your waking hours studying math. [It could happen!] So you just
unpack them and stack them in the corner. How high will this stack be after ...
one month?
three months?
six months?
a year?
Here are some useful distances for comparison.
12 inches = 1 foot
300 feet = 1 football field
5280 feet = 1 mile
3,300 miles = OR to FL
250,000 miles = earth to moon
93,000,000 miles = earth to sun